On the Asymptotic Distribution of LRT When Parameters Lie on the Boundary

• Activity Number: 476
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Bimal K. Sinha*+ and Leonid Kopylev
• Companies: U.S. Environmental Protection Agency and U.S. Environmental Protection Agency
• Keywords: asymptotic distribution ; likelihood ratio test ; parameter on boundary ; mixture of chisquares

Abstract

The paper discusses statistical inference dealing with the asymptotic theory of likelihood ratio tests when some parameters lie on the boundary. We derive a closed form solution when one parameter of interest and one nuisance parameter lie on the boundary. The asymptotic distribution is a mixture of several chi-square distributions. For the cases when one parameter of interest and two nuisance parameters or two parameters of interest and one nuisance parameter are on the boundary, we provide an explicit solution which can be easily computed by simulation. These results can be used in many applications and we discuss two: construction of one-sided confidence bounds by profile likelihood in environmental risk assessments and testing for random effects in genetics.